Agriculture Reference
In-Depth Information
length of latent period generally depends on temperature for most pathogens (Shaw,
1990; Davis and Fitt, 1994; Wadia and Butler, 1994; Webb and Nutter, 1997;
Viljanen-Rollinson
et al.
, 1998; Xu, 1999b; Xu and Robinson, 2000, 2001). At the
same time, weather conditions may affect the rate of fungicide decay, and in turn
affect disease development. Further research is needed to investigate the severity of
potential errors in conclusions drawn from models that assume a constant rate.
Campbell and Madden (1990) proposed a simple method to model a variable
rate; they treated the rate parameter (
r
) as a specific function of time. This rate
function can then be incorporated into any growth model. The rate parameter has
also been expressed directly as a sinusoidal function of temperature in a logistic
model (Waggoner, 1986). Another approach was taken to model a variable rate in
order to understand the temporal spread of African cassava mosaic virus (Fargette
and Vie, 1994; see also Chapter 20); they treated the rate as a product of two
functions: one described the effects of the age and the other the effect of season on
disease development.
(c) Disease components
Simple growth models when used to describe temporal disease progress have an
inherent limitation in that they assume that the rate of absolute disease increase at a
particular time is a function of the total disease at that time. However, not all lesions
produce spores that may cause new infections at a given time; the absolute rate of
disease increase does not depend on the total disease already present but on the
proportion of the total diseased tissues that are producing viable spores. In order to
overcome this limitation, we need to define age classes for diseases. Commonly,
three important classes are defined: latent, infectious and removed. The period of
time between initial infection and when new infections produce infective propagules
(i.e. become infectious) is called the latent period; the period of time a single lesion
can produce infectious propagules is called the infectious period; finally post-
infectious disease is called removed.
A corrected basic infection rate (
R
) was proposed to take into account different
classes of diseases (Van der Plank, 1963). A modified logistic model can be written
as
dy
dt
(
)
(8.6)
(
)
=
Ry
t
−
p
−
y
t
−
i
−
p
1
−
y
t
where
i
and
p
are the length of infectious and latent periods, respectively. Thus, the
absolute rate of change in disease depends on the amount of infectious disease (
y
t-p
-
y
t-i-p
) as well as total healthy susceptible area. The
R
parameter is related to the
apparent infection rate (
r
):
r
y
(8.7)
R
=
t
y
y
−
t
−
p
t
−
i
−
p
